Civil Engineering Tools
BeamTrussMohr's CircleUnit ConversionsCentroidDeflectionBucklingConcreteRebarFE Prep

Average Wait Time in an M/M/1 Queue

Hardqueueingtraffic
Vehicles arrive at a toll booth at 500 per hour and are served at 600 per hour, both Poisson distributed. Modelled as an M/M/1 queue, the average time a vehicle spends in the system is most nearly:
  1. A6 seconds
  2. B36 seconds
  3. C60 seconds
  4. D300 seconds
Show solution

Answer: B. 36 seconds

For an M/M/1 queue the average time in the system is w = 1/(μ − λ) = 1/(600 − 500) = 0.01 hour = 36 seconds. Note how sensitive this is to utilisation: raising arrivals to 550 per hour would double the delay, which is why booths congest sharply near capacity.
Practice this deckUntimed, one problem at a time, with your progress saved.

Related problems

Keep studying